problem solving using 4 operations

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4 Operations: Mixed word problems

Add / subtract / multiply / divide.

Students use the 4 basic operations (addition, subtraction, multiplication and division) to solve these word problems. Some questions will have more than one step. Mixing word problems encourages students to read and think about the questions rather than recognizing a pattern to the solutions.

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4th Grade Resources - Use the four operations with whole numbers to solve problems.

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Newest 4th Grade Resources - Use the four operations with whole numbers to solve problems.

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Operator Arithmetic

Use the four operators to solve multi-step equations

Mixed matching

Match pairs of equivalent equations to score points

Balloon Pop Mixed Operators

Pop ballons with mixed operators from smallest to largest

Calculator Chaos

Use knowledge of operations to solve several math problems using a single set of numbers.

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Common Core: 3rd Grade Math : Solving Problems Involving the Four Operations, and Identifying and Explaining Patterns in Arithmetic

Study concepts, example questions & explanations for common core: 3rd grade math, all common core: 3rd grade math resources, example questions, example question #1 : solve two step word problems using the four operations: ccss.math.content.3.oa.d.8.

Example Question #2 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

Example Question #1 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

Example Question #4 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

Example Question #5 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

Now we need to add the watermelon, strawberries, and raspberries together to find our total. 

Example Question #2 : Solve Two Step Word Problems Using The Four Operations: Ccss.Math.Content.3.Oa.D.8

Example Question #7 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

To find the total number of flyers that she hung we add the amount of flyers on the east side and the amount on the west side. 

Example Question #8 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

Example Question #9 : Solving Problems Involving The Four Operations, And Identifying And Explaining Patterns In Arithmetic

Now we need to add up our number of balls, stuffed animals and ropes to find our total. 

To find the total amount of laps that he swam, we need to add up the laps that he did each day. 

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The Four Operations

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Four Operations Problems

Fourth grade four operations problems.

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Worksheet on Word Problems on Four Operations

Practice the questions given in the worksheet on word problems on four operations i.e. addition (+), subtraction (-), multiplication (×) and division (÷).

Solve the following:

1.  The population of a town is 198568. Out of them 45312 are men and 35678 are women. Find the number of children in the town.

2.  A shopkeeper has 2425 boxes of 24 pencils each. How many pencils do all the boxes have in all?

3.  Linda bought a coat for $2265 and a saree for $2150. She gave $5000 to the shopkeeper. How much money did the shopkeeper return to her?

4.  The cost of 21 TV sets is $95844. Find the cost of one TV set.

5.  A factory produces 24532 bulbs in a month. What is its annual production?

6. There are 145968 bags of sugar, 236487 bags of wheat and some bags of rice in a godown. It the total number of bags in the godown is 450000, find the number of bags of rice.

7. A factory manufactured 483685 toys in three weeks. The production in first week was 146345 toys and in second week 138152 toys. Find the production in the third week.

8. The cost of a sofa set is $9372. How much will 124 such sofa sets cost?

9. There are 86 rooms in a school. 4386 students study there. Equal number of students sits in each room?

10. 1575 students of a school want to go Agra by bus. If one bus can carry 75 students, how many buses are required to carry all the students?

11. The cost of a radio set is 1475. What is the cost of 35 such radio sets?

12. In an election, 52496 people voted for Ron, 44929 people for Jhon and 36824 people for Mike in a town. If everyone voted in the town, what is the total number of voters?

13. Maria bought 96 toys priced equally for $12960. The amount of $1015 is still left with her. Find the cost of each toy and the amount she had.

Answers for the worksheet on word problems on four operations are given below to check the exact answers of the above questions on addition, subtraction, multiplication and division.

1. 117578 children.

2. 58200pencils.

5. 294384 bulbs.

6. 67545 bags.

7. 199188 toys.

8. $1162128

9. 51 students.

10. 21 buses.

13. $135, $13975

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2-Step Problems using 4 Operations Worksheets

Related Pages Math Worksheets Lessons for Third Grade Free Printable Worksheets

Printable “Word Problems” Worksheets Addition Word Problems 2nd Grade Word Problems Add/Subtract Word Problems Multiply/Divide Word Problems Word Problems using 4 Operations

Printable worksheets to help students solve 3rd grade word problems by representing the information in the problems visually with the help of tape diagrams or bar models. (Solve two-step word problems involving all four operations: addition, subtraction, multiplication, and division)

Using tape diagrams, also known as bar models, is an effective visual strategy for solving two-step problems involving the four basic operations. Here’s a step-by-step guide on how to solve 2-step problems using tape diagrams:

Read and Understand the Problem: Carefully read the problem to understand the context and identify the information given and what needs to be found.

Identify the Operations: Determine which operations (addition, subtraction, multiplication, or division) are involved in the problem. Look for keywords that indicate each operation.

Break Down into Steps: Identify the main steps or operations required to solve the problem.

Draw the Tape Diagram: Represent the situation using a tape diagram. Use rectangles to represent quantities and label them accordingly.

Verify that your solution makes sense in the context of the problem. Check your calculations for accuracy.

Click on the following worksheet to get a printable pdf document. Scroll down the page for more 2-Step Problems using 4 Operations Worksheets .

More 2-Step Problems using 4 Operations Worksheets

Printable (Answers on the second page) 2-Step Problems Worksheet #1 2-Step Problems Worksheet #2 2-Step Problems Worksheet #3 2-Step Problems Worksheet #4 2-Step Problems Worksheet #5 2-Step Problems Worksheet #6 2-Step Problems Worksheet #7 2-Step Problems Worksheet #8 2-Step Problems Worksheet #9

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WORD PROBLEMS - using all four operations

Subject: Mathematics

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22 September 2020

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Four Operations in Math

The four basic operations in math are addition, subtraction, multiplication, and division. These operations form the foundation of arithmetic and are essential for performing calculations and solving problems in various fields. In this article, we'll explore the principles, properties, and applications of each operation.

Four Operations Calculator

Addition is the process of combining two or more numbers to find their total, called the sum. This operation is represented by the plus symbol (+). For example:

Addition has the following properties:

• Commutative: a + b = b + a
• Associative: (a + b) + c = a + (b + c)
• Identity: a + 0 = a

Addition Calculations :

Subtraction.

Subtraction is the process of finding the difference between two numbers. This operation is represented by the minus symbol (-). For example:

Subtraction has the following properties:

• Non-commutative: a - b ≠ b - a (in general)
• Non-associative: (a - b) - c ≠ a - (b - c) (in general)
• Identity: a - 0 = a

Subtraction Calculations :

Multiplication.

Multiplication is the process of finding the product of two numbers. This operation is represented by the multiplication symbol (×) or an asterisk (*). For example:

Multiplication has the following properties:

• Commutative: a * b = b * a
• Associative: (a * b) * c = a * (b * c)
• Identity: a * 1 = a
• Distributive: a * (b + c) = a * b + a * c

Multiplication Calculations :

Division is the process of finding the quotient of two numbers, dividing one number by another. This operation is represented by the division symbol (÷) or a forward slash (/). For example:

Division has the following properties:

• Non-commutative: a / b ≠ b / a (in general)
• Non-associative: (a / b) / c ≠ a / (b / c) (in general)
• Identity: a / 1 = a
• Undefined for division by zero: a / 0 is undefined

Division Calculations :

Applications of the four operations.

The four basic operations are used in a wide range of mathematical and real-world applications, including:

• Calculating totals, change, and discounts in finance
• Measuring distances, areas, and volumes in geometry
• Deriving equations and solving problems in algebra
• Analyzing data and calculating probabilities in statistics
• Modeling scenarios and making predictions in various fields

The four basic operations in math - addition, subtraction, multiplication, and division - are fundamental to arithmetic and problem-solving. Understanding their principles, properties, and applications is essential for success in mathematics and various real-world contexts.

How To Use Fractions In 4-Operations

To add fractions, make sure the denominators are the same. Add the numerators together and keep the denominator the same. Simplify the result if needed.

Subtraction:

Similar to addition, ensure the denominators are identical. Subtract the numerators while keeping the denominator constant. Simplify the result if necessary.

Multiplication:

Multiply the numerators together to get the new numerator. Multiply the denominators together to get the new denominator. Simplify the resulting fraction if possible.

To divide fractions, multiply by the reciprocal of the second fraction. Invert the second fraction (swap the numerator and denominator). Then, follow the steps for multiplication.

Fractions Operations :

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Problem Solving Using the Four Operations

Primary Standards:

MAFS.3.OA.4.8 Solve two-step word problems using the four (addition or subtraction) operations. Represent these problems using equations with a letter (symbol) standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

MAFS.3.OA.1.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Connecting Standards:

MAFS.3.OA.1.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = [] ÷ 3, 6 × 6 = ?.

Content Knowledge:

In prior grades, students solved a variety of one- and two-step word problems using addition or subtraction.  In 3 rd grade, with the introduction of multiplication and division, they will be challenged to solve one- and two-step problems with all four of the operations.

Knowing which operation makes sense to solve a problem is a foundational problem-solving skill.  This is not achieved by identifying key words that tell students what to do, but instead, by recognizing the story situation or structure.  When students understand what is happening in a story problem and know the actions of the operations, they are able to match the operation to the problem situation.

A critical skill in solving word problems is the ability to represent the problem situation with equations.  In prior situations, students used symbols such as a blank space, a box, or a question mark to represent missing information.  In 3 rd grade, they are introduced to the use of a letter to stand of unknowns in equations.  Students may be accustomed to representing a problem with an equation, but in two-step problems they may need to build two equations as they work through the steps of the problem.

GCG 1 – Learning Goal:  As a mathematician, I will be able to model and solve one-step problems; represent problems using equations with a letter for the unknown

• Step 1: Represent a problem-solving situation with an equation, using a letter for the unknown
• Step 2: Solve one-step equations, using a letter for the unknown

GCG 2 – Learning Goal:  As a mathematician, I will be able to model and solve two-step problems; represent problems using equations with a letter for the unknown

• Step 1: Explain and directly model the steps of a two-step problem with concrete models or drawings
• Step 2:  Represent a two-step problem-solving situation with an equation (or equations), using a letter for the unknown
• Step 3: Solve two-step problems using models, drawing, or equations

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Anticipate, accommodate, empower

Exploring generative ai at harvard.

Jessica McCann

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Leaders weigh in on where we are and what’s next

The explosion of generative AI technology over the past year and a half is raising big questions about how these tools will impact higher education. Across Harvard, members of the community have been exploring how GenAI will change the ways we teach, learn, research, and work.

As part of this effort, the Office of the Provost has convened three working groups . They will discuss questions, share innovations, and evolve guidance and community resources. They are:

• The Teaching and Learning Group , chaired by Bharat Anand , vice provost for advances in learning and the Henry R. Byers Professor of Business Administration at Harvard Business School. This group seeks to share resources, identify emerging best practices, guide policies, and support the development of tools to address common challenges among faculty and students.
• The Research and Scholarship Group , chaired by John Shaw , vice provost for research, Harry C. Dudley Professor of Structural and Economic Geology in the Earth and Planetary Sciences Department, and professor of environmental science and engineering in the Paulson School of Engineering and Applied Science. It focuses on how to enable, and support the integrity of, scholarly activities with generative AI tools.
• T he Administration and Operations Group , chaired by Klara Jelinkova , vice president and University chief information officer. It is charged with addressing information security, data privacy, procurement, and administration and organizational efficiencies.

Klara Jelinkova, Bharat Anand, and John Shaw.

Photos by Kris Snibbe/Harvard Staff Photographer; Evgenia Eliseeva; and courtesy of John Shaw

The Gazette spoke with Anand, Shaw, and Jelinkova to understand more about the work of these groups and what’s next in generative AI at Harvard.

When generative AI tools first emerged, we saw universities respond in a variety of ways — from encouraging experimentation to prohibiting their use. What was Harvard’s overall approach?

Shaw: From the outset, Harvard has embraced the prospective benefits that GenAI offers to teaching, research, and administration across the University, while being mindful of the potential pitfalls. As a University, our mission is to help enable discovery and innovation, so we had a mandate to actively engage. We set some initial, broad policies that helped guide us, and have worked directly with groups across the institution to provide tools and resources to inspire exploration.

Jelinkova: The rapid emergence of these tools meant the University needed to react quickly, to provide both tools for innovation and experimentation and guidelines to ensure their responsible use. We rapidly built an AI Sandbox to enable faculty, students, and staff to experiment with multiple large language models in a secure environment. We also worked with external vendors to acquire enterprise licenses for a variety of tools to meet many different use cases. Through working groups, we were able to learn, aggregate and collate use cases for AI in teaching, learning, administration, and research. This coordinated, collective, and strategic approach has put Harvard ahead of many peers in higher education.

Anand: Teaching and learning are fundamentally decentralized activities. So our approach was to ask: First, how can we ensure that local experimentation by faculty and staff is enabled as much as possible; and second, how can we ensure that it’s consistent with University policies on IP, copyright, and security? We also wanted to ensure that novel emerging practices were shared across Schools, rather than remaining siloed.

What do these tools mean for faculty, in terms of the challenges they pose or the opportunities they offer? Is there anything you’re particularly excited about?

Anand: Let’s start with some salient challenges. How do we first sift through the hype that’s accompanied GenAI? How can we make it easy for faculty to use GenAI tools in their classrooms without overburdening them with yet another technology? How can one address real concerns about GenAI’s impact?

While we’re still early in this journey, many compelling opportunities — and more importantly, some systematic ways of thinking about them — are emerging. Various Harvard faculty have leaned into experimenting with LLMs in their classrooms. Our team has now interviewed over 30 colleagues across Harvard and curated short videos that capture their learnings. I encourage everyone to view these materials on the new GenAI site; they are remarkable in their depth and breadth of insight.

Here’s a sample: While LLMs are commonly used for Q&A, our faculty have creatively used them for a broader variety of tasks, such as simulating tutors that guide learning by asking questions, simulating instructional designers to provide active learning tips, and simulating student voices to predict how a class discussion might flow, thus aiding in lesson preparation. Others demonstrate how more sophisticated prompts or “prompt engineering” are often necessary to yield more sophisticated LLM responses, and how LLMs can extend well beyond text-based responses to visuals, simulations, coding, and games. And several faculty show how LLMs can help overcome subtle yet important learning frictions like skill gaps in coding, language literacy, or math.

Do these tools offer students an opportunity to support or expand upon their learning?

Anand: Yes. GenAI represents a unique area of innovation where students and faculty are working together. Many colleagues are incorporating student feedback into the GenAI portions of their curriculum or making their own GenAI tools available to students. Since GenAI is new, the pedagogical path is not yet well defined; students have an opportunity to make their voices heard, as co-creators, on what they think the future of their learning should look like.

Beyond this, we’re starting to see other learning benefits. Importantly, GenAI can reach beyond a lecture hall. Thoughtful prompt engineering can turn even publicly available GenAI tools into tutorbots that generate interactive practice problems, act as expert conversational aids for material review, or increase TA teams’ capacity. That means both that the classroom is expanding and that more of it is in students’ hands. There’s also evidence that these bots field more questions than teaching teams can normally address and can be more comfortable and accessible for some students.

Of course, we need to identify and counter harmful patterns. There is a risk, in this early and enthusiastic period, of sparking over-reliance on GenAI. Students must critically evaluate how and where they use it, given its possibility of inaccurate or inappropriate responses, and should heed the areas where their style of cognition outperforms AI. One other thing to watch out for is user divide: Some students will graduate with vastly better prompt engineering skills than others, an inequality that will only magnify in the workforce.

What are the main questions your group has been tackling?

Anand: Our group divided its work into three subgroups focused on policy, tools, and resources. We’ve helped guide initial policies to ensure safe and responsible use; begun curating resources for faculty in a One Harvard repository ; and are exploring which tools the University should invest in or develop to ensure that educators and researchers can continue to advance their work.

In the fall, we focused on supporting and guiding HUIT’s development of the AI Sandbox. The Harvard Initiative for Learning and Teaching’s annual conference , which focused exclusively on GenAI, had its highest participation in 10 years. Recently, we’ve been working with the research group to inform the development of tools that promise broad, generalizable use for faculty (e.g., tutorbots).

What has your group focused on in discussions so far about generative AI tools’ use in research?

Shaw: Our group has some incredible strength in researchers who are at the cutting edge of GenAI development and applications, but also includes voices that help us understand the real barriers to faculty and students starting to use these tools in their own research and scholarship. Working with the other teams, we have focused on supporting development and use of the GenAI sandbox, examining IP and security issues, and learning from different groups across campus how they are using these tools to innovate.

Are there key areas of focus for your group in the coming months?

Shaw: We are focused on establishing programs — such as the new GenAI Milton Fund track — to help support innovation in the application of these tools across the wide range of scholarship on our campus. We are also working with the College to develop new programs to help support students who wish to engage with faculty on GenAI-enabled projects. We aim to find ways to convene students and scholars to share their experiences and build a stronger community of practitioners across campus.

What types of administration and operations questions are your group is exploring, and what type of opportunities do you see in this space?

Jelinkova: By using the group to share learnings from across Schools and units, we can better provide technologies to meet the community’s needs while ensuring the most responsible and sustainable use of the University’s financial resources. The connections within this group also inform the guidelines that we provide; by learning how generative AI is being used in different contexts, we can develop best practices and stay alert to emerging risks. There are new tools becoming available almost every day, and many exciting experiments and pilots happening across Harvard, so it’s important to regularly review and update the guidance we provide to our community.

Can you talk a bit about what has come out of these discussions, or other exciting things to come?

Jelinkova: Because this technology is rapidly evolving, we are continually tracking the release of new tools and working with our vendors as well as open-source efforts to ensure we are best supporting the University’s needs. We’re developing more guidance and hosting information sessions on helping people to understand the AI landscape and how to choose the right tool for their task. Beyond tools, we’re also working to build connections across Harvard to support collaboration, including a recently launched AI community of practice . We are capturing valuable findings from emerging technology pilot programs in HUIT , the EVP area , and across Schools. And we are now thinking about how those findings can inform guiding principles and best practices to better support staff.

While the GenAI groups are investigating these questions, Harvard faculty and scholars are also on the forefront of research in this space. Can you talk a bit about some of the interesting research happening across the University in AI more broadly ?

Shaw: Harvard has made deep investments in the development and application of AI across our campus, in our Schools, initiatives, and institutes — such as the Kempner Institute and Harvard Data Science Initiative. In addition, there is a critical role for us to play in examining and guiding the ethics of AI applications — and our strengths in the Safra and Berkman Klein centers, as examples, can be leading voices in this area.

What would be your advice for members of our community who are interested in learning more about generative AI tools?

Anand: I’d encourage our community to view the resources available on the new Generative AI @ Harvard website , to better understand how GenAI tools might benefit you.

There’s also no substitute for experimentation with these tools to learn what works, what does not, and how to tailor them for maximal benefit for your particular needs. And of course, please know and respect University policies around copyright and security.

We’re in the early stages of this journey at Harvard, but it’s exciting.

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